The structure of crystalline materials can be analyzed using diffraction methods, wherein suitable waves are coherently scattered by the atoms of the material. The direction-dependent intensity of the scattered radiation is then recorded at different scattering angles. Various information on the crystalline material, such as on the crystal structure, chemical bonds or mechanical strain within the sample, can be derived from the recorded angle-dependent intensity distribution of the diffracted waves of the radiation applied.
Suitable radiation can either be electromagnetic radiation, such as X-rays, or massive particle radiation, such as electron or neutron beams, as long as the wavelength of the radiation is within the magnitude of the lattice constant(s) of the structure(s) to be analyzed. While X-ray crystallography still is one of the most widely used techniques in structure analysis, more and more methods utilizing electron beams for resolving crystal structures are developed, as at least some of these methods can be functionally integrated in electron microscopes.
Diffraction patterns of an analyzed sample are often recorded using photodetectors, either alone or in combination with a scintillation screen. With a two-dimensional detector surface only a two-dimensional projection, e.g. a gnomonic projection, of a diffraction pattern directed from the sample into all three dimensions can be recorded. In order to interpret the recorded projected intensities, it is necessary to know the mathematical parameters of the projection function from the three-dimensional to the two-dimensional space. In case of the gnomonic projection, which projects 3D directions on a sphere to 2D points on a plane, the position of the central point of the projection (i.e. the center of the sphere) needs to be known relative to the projection plane. In measurements of diffracted intensities, this so-called pattern center (PC) can correspond to a sample region onto which an incident probe beam is directed and from which the diffracted radiation is emitted into all directions and collected on a planar screen.
In electron backscatter diffraction (EBSD) a crystalline sample is placed in a scanning electron microscope (SEM) and irradiated with a focused electron beam. At least part of the electrons are scattered within the sample and then exit it with an angle-dependent intensity distribution. Using a two-dimensional detector, Kikuchi patterns can be recorded in a gnomonic projection on the detector surface. The backscattering of the incident electrons takes place within a limited region near the incident electron beam position. The position of this source region of the diffraction pattern with respect to the detector surface is the so-called pattern center (PC).
Maurice et al. disclosed a moving screen method for accurate localization of the pattern center of diffraction patterns in EBSD. Therein two diffraction patterns are obtained with two relative positions of detector screen and sample and are thus optically zoomed relative to each other. One of the patterns is then virtually zoomed, i.e. the projection center coordinates are varied, until the cross-correlation with the other pattern reaches a maximum. By comparison of the virtually zoomed and the optically zoomed pattern, a shift value for determining the pattern center relative to the image center can be obtained (C. Maurice, K. Dzieciol, R. Fortunier, Ultramicroscopy) 111, 140 (2011)).
Biggin and Dingley disclosed a method for locating a source point of X-rays in a Kossel diffraction method that shall be applicable to any point-source method, where a pattern center is required. According to the method, spherical balls of steel are placed between the sample and the detector during an otherwise normal recording of a Kossel diffraction pattern. The balls block the radiation from the X-ray source, and thus cast shadows that form ellipses with major axes intersecting at the pattern center (S. Biggin, D. J. Dingley, J Appl Crystallogr 10, 376 (1977)).
The known methods are each prone to a variety of systematic errors and cannot be easily introduced in a standard SEM that is designed for multiple uses. The accuracy in determining the pattern center usually converges at around 0.5 to 1% of the pattern width. The objective of the present invention is to avoid or at least reduce one or more drawbacks of the prior and to provide a method for localizing a radiation source with improved accuracy that can be easily integrated in various structure analysis apparatuses.